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I have tweaked the Idea-section at naturalness, and I added a pointer to the first decent discussion that I have seen: Clarke 17
I have added, below the quote from Wilson 04, also quotes from Kane 17: here
I wonder if the alternatives are merely naturalness and having a theory. Doesn’t one always have expectations given a theoretical framework, and when some observation appears unlikely, it’s probably time to change the framework? So naturalness is always relative to some theory.
We see at the moment at large-scale how a decade-old edifice of non-rigorous, essentially numerological, arguments, is dissolving into thin air, leaving a large part of HEP “theory” in an unprecedented state of puzzlement about their own previous claims. The worst aspect of it is that also reasonble arguments in the vicinity are torn down together with the sinking ship. It is a striking symptom of the situation that Kane’s school, with its emphasis of focusing on computation from first principles, plays the outsider position.
To play devil’s advocate, I see Kane doesn’t cite his own predictions when discussing the low-energy superpartners that didn’t get seen. I can’t recall off-hand if he used to use naturalness as a technique to predict stuff.
David, if you are interested in going beyond what the blogs offer, I suggest having a closer look. Dating way back from rev 4 due to somebody signing as Otto, we have a pretty decent brief survey of the generic properties of the G2-MSSM.
Of course getting out concrete numbers requires putting in concret numbers, or else you are dreaming a Douglas Adams novel.
I did say “devil’s advocate” :-)
Also, I think our comments crossed paths. I was thinking Kane had perhaps jumped ship from the naturalness idea and was now promoting something else, but this (=specific model-building with the aim of arriving ab initio at generic SM-like properties) may have been his approach the whole time. I haven’t dug through the literature.
Sabine Hossenfelder makes the point:
That you have to hand-select a probability distribution to make naturalness well-defined used to be well-known. One of the early papers on the topic clearly states
“The “theoretical license” at one’s discretion when making this choice [for the probability distribution] necessarily introduces an element of arbitrariness to the construction.” Anderson and Castano, Phys. Lett. B 347:300-308 (1995)
and
I believe what is needed for progress in the foundations of physics is more mathematical rigor. Obsessing about ill-defined criteria like naturalness that don’t even make good working hypotheses isn’t helpful. And it would serve particle physicists well to identify their previous mistakes in order to avoid repeating them. I dearly hope they will not just replace one beauty-criterion by another.
There are a lot of phrases and words at G2-MSSM that an energetic student could start writing stubs for (eg: Pecchei-Quinn-type shift symmetry, hierarchy, hidden sector, soft supersymmetry breaking terms, slightly [?] split spectrum, generic bottom-up Split Supersymmetry scenario, protected, suppressed, generated non-thermally, late-time moduli decays). It’s this type of jargon that makes the field mildly incomprehensible. Ditto when Jacques D starts giving reasons he isn’t happy with, for example, higher gauge theory; he may be completely correct, but a lot of it requires a lot more than what I currently know in order to parse it.
Ditto when Jacques D starts giving reasons he isn’t happy with, for example, higher gauge theory; he may be completely correct, but a lot of it requires a lot more than what I currently know in order to parse it.
Interesting that you mention this. When I have glanced at his (and the other string theorists’) recent comments on the n-café, my thoughts were: this sounds like pseudo-science, not science. Lots of unknown words bound up occasionally with words that have a precise mathematical meaning (like moduli space). Maybe an expert can make sense of it, but it looks like mathematical fiction to an outsider. In particular, it is hardly surprising (again, to an outsider) that disagreements and misunderstandings arise if the mathematics is not usually made more precise than in those comments when string theorists communicate with one another.
Here is a talk by Hopkins where he remarks on physicists’ use of the word “model” (eg Landau-Ginzburg model, A-model, B-model, Sigma-model), which seems to me to be used in a way that seems like it should be covered by the Stewart test. One that arose in recent discussion^{1} at the Café was “Coulomb branch”, and then Teleman came out with this paper that at least uses some serious mathematics to describe such objects.
A sample of Jacques’ writing that I think Richard is probably describing: “With some abuse of nomenclature, this is usually called the Coulomb branch. At a generic point on the Coulomb branch the 5D gauge symmetry is broken to the Cartan. The gauge bosons corresponding to the broken generators are massive and their masses are BPS-protected, so their tree-level dependence on the Yang-Mills coupling is exact.” Again, this all probably has reasonably well-defined meaning, but it’s the kind of thing that seems to be learned by osmosis. ↩
We have a page Coulomb branch, so I’ve added the Teleman paper. I don’t see that there’s anything worse going on than people showing their usual reluctance to learn each other’s languages.
That’s possible. I should just pipe up next time and ask for a reference where the material is defined.
There are a lot of phrases and words
Here is some dictionary:
Pecchei-Quinn-type shift symmetry,
This means that fields take periodic values, hence that if you think of them as $\mathbb{R}$-valued, they are actually $\mathbb{R}/\mathbb{Z}$-valued.
This was postulated as a property of axions in order that they solve the strong CP-problem. The neat thing here is that such behaviour is exactly what one sees for higher gauge fields: If their $p+1$-form curvature vanishes their gauge equivalence classes are in $H^{p}(X,U(1))$ by the curvature exact sequence (this prop.).
In the $G_2$-MSSM the main higher gauge field is the supergravity C-feld with $p = 3$, and the statement is that after KK-reduction this neatly exhibits the axionic properties that Pecchei-Quinn had to pull out of thin air.
hierarchy,
This means that ratios of the characteristic mass scales of the theory (usually the Planck mass compared to the Higgs mass/electroweak symmetry breaking scale) are many orders of magnitude.
hidden sector,
If the field content of a field theory may be divided into two components such that the only interaction between fields in one component with those in the other is by gravity, then these two are “hidden” to each other. If one matches one of the components to observable phenomenology, this means that the fields in the other components are literally invisible in the world thus described, except for their pull of gravity.
Hidden sectors have been postulated as ways to explain supersymmetry breaking (called “gravity mediated susy breaking”) and other things. A standard example where they appear naturally is Horava-Witten compactification of M-theory in an interval, which manifestly features two copies of heterotic gauge theory at each end of the “interval”, interacting only via gravity in the 11d bulk spacetime.
slightly [?] split spectrum,
The term “split supersymmetry” refers to scenarios where the superpartner masses are immensely higher than that of the seen particles. Way above the TeV scale. The “slightly split” spectrum here means that some of the superpartners are right about at a TeV, whereas the rest is way up higher.
With present experimental data it’s the split and slightly-split models of “low energy” susy that survive, the rest being ruled out.
Similarly to the shift periodicity of the axion fields, split supersymmetry was originally postulated in an ad-hoc manner and seemed contrived, but comes out naturally in the $G_2$-MSSM.
generic bottom-up
In particle physic model building they say “bottom up” when they first cook up some particle content which they are interested in considering, and then try to see if this can be embedded in a consistent theory, while they say “top down” if they start with a theory and then deduce its consequences.
protected,
If a symmetry is imposed as a renormalization condition it constrains the space of renormalization choices. Sometimes it constrains it so much that certain observables no longer have any renormalization choices. In this case one says they are “protected” from renormalization by the symmetry. This allows to compute these observables in the classical theory and be assured that the result is also the correct value in the quantum theory.
suppressed,
Some quantity $A$ that comes with an exponential prefactor with negative exponent, $e^{-q} A$ is suppressed by $q$.
Started something at protection from quantum corrections
Awesome, thanks!
Started something at hidden sector.
By the way, regarding this side remark in #7:
when Jacques D starts giving reasons he isn’t happy with, for example, higher gauge theory;
I think you must be misreading the comment. He coauthored one of the deepest applications of higher gauge theory to type II strings in 09, jointly with D. Freed, who was maybe the first to fully highlight the role of higher gauge theory in string theory in the first place.
In that discussion the issue is instead a specific one, concerning just the subtle nature specifically of the 2-form field in the expected 6d worldvolume theory of coincident M5-branes.
Perhaps David R. is picking up on the difficulty Jacques expressed in understanding (“$n$-groups (whatever those are)”) and
I described the idea in Section 3 of my paper with Mike Shulman called Lectures on $n$-categories and cohomology, though probably not in a very physicist-friendly manner.
That’s putting it mildly.
To wrap my head around it, it would be helpful (maybe a future blog post?) to spell out the Potsnikov data associated to some of Tachikawa’s examples.
More generally, if one delves a little deeper, one runs into more general relative field theories than your run-of-the-mill anomalous theories (theories relative to a $(d+1)$-dimensional invertible field theory) when studying the “obstruction to gauging” some (possibly higher) symmetry.
I pointed him to the relevant section of twisted smooth cohomology in string theory
I imagine the Tachikawa paper is the one I mentioned on the other thread:
Regarding #9: thanks David R, yes, that is a good choice of example of the kind of passage I was thinking of.
I don’t see that there’s anything worse going on than people showing their usual reluctance to learn each other’s languages.
Indeed, I assume that to an expert the language in the comment that David R quoted all makes sense and is meaningful. Still, amongst the string theorists contributing to that discussion, there seemed to be some problem in understanding one another. It seemed rather ironic that assertions were being made rather forcefully when the whole thing looked rather fanciful to an untrained eye! But, as you suggest, that impression of fancifulness could well be largely or entirely a matter of unfamiliarity with the language on my part.
It seemed rather ironic that assertions were being made rather forcefully when the whole thing looked rather fanciful to an untrained eye!
That is indeed a major problem with the whole field in general and with its vocal members in particular. While the superficial impression that the bystanding mathematician may get, that it is all gobbledygook, is not justified, what is true is that the HEP physics community is completely lacking a decent discussion culture that would allow participants to proceed with care, in public, without feeling risk for their reputation.
For years the discussion of research-level mathematics on the web is blossoming, while that in HEP physics is stagnating on the lowest possible level of self-parody. Any time a serious research-level discussion in hep physcis shows a tentative inclination to begin somewhere on the web, the usual suspects and their larger-than-life egos jump in and try to ellbow each other out of the way by iterated proof-by-intimidation.
Thank you very much for this! Let us hope that your continued efforts gradually effect a change for the better. David C pointed to a few things on the n-café that seem to suggest that the nLab may slowly be beginning to become a resource which helps enables this.
Perhaps David R. is picking up on the difficulty Jacques expressed in understanding
Don’t be fooled. He goes on about Postnikov data.
Yes, but John Baez had just been just been explaining about Postnikov data.
Still maybe he’s playing down what he knows.
David, just search for “Postnikov” in arXiv:0906.0795, arXiv:hep-th/0701244 and so forth.
Well it’s all a mystery to me. I dare say the younger ones, like Tachikawa (#17) and Monnier (worked with Gregory Moore at Rutgers, but now seems to be in the maths department at Geneva), will turn first.
Hamiltonian anomalies from extended field theories acknowledges the nLab as
a very useful reference for many of the higher categorical concepts appearing in the present paper,
and the author knows of the larger picture:
Our construction generalizes the construction of the classical Dijkgraaf-Witten theory by Freed… and is strongly inspired by this work. Note that such theories have been constructed using elaborate technology under the name of $\infty$-Chern-Simons theories.
Thanks for the pointer, I had actually missed both of these passages in the article.
But I am happy to have invited Samuel Monnier to a “Durham Syposium” that we are organizing later this year, “Higher Structures in M-Theory” (not much online at the moment, just the brief item 109 in the table here)
continuing with the requested dictionary as in #12 and below: have started something at split supersymmetry
one more dictionary item as in #12: bottom-up and top-down model building
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